Some metallic materials in tension and geomaterials in compression exhibit a descending segment on the load-displacement diagram. The model of the strain-softening rate insensitive elasto-plastic solid conventionally describes constitutive behavior of such materials. If the process of deformation took place at the descent segment of the stress-strain diagram the governing equations would change their type and the initial boundary-value problem become ill-posed. However it never happens in the properly posed physical problems. It is proved that continuous deformations in the region of softening are unstable. Instability leads to a dynamical process even in the case of quasistatic external loading. Deformations corresponding to the descent part of the stress-strain diagram are localized at the surfaces, lines or points depending on the dimension of the problem under consideration. Localization of deformations produces unloading that provokes propagation of shock waves of unloading and secondary hardening. The fundamental laws of conservation and balance combined with the initial and boundary conditions constitute well-posed mathematical problem. As an illustrative example the problem of quasistatic displacement controlled stretching of an elasto-plastic bar with partial softening is considered. Usage of the model of an elasto-visco-plastic softening solid permits to study evolution of strain localization. In this case the post critical process is also dynamic but the governing equations are hyperbolic and problem is well posed even for deformation on the descent segment. Stretching with of constant velocity of the end of a rod leads to localization of deformation in a small length depending on velocity and approaching zero when velocity vanishes. Stretching with constant stress of the end of a rod also leads to localization of deformation but region of localization linearly grows with time. As an alternative to a softening solid a model of material with structural transformation of a solid into another solid with different mechanical properties and natural stress state is proposed and analyzed. Conditions at the front of a shock wave of structural transformation include equation of energy. It is shown that depending on material properties structural transformation may be both static and dynamic.
J. R. Rice discovered, during computer simulation, the existence of a wave that could propagate, apparently without change of form and without attenuation, along the edge of a propagating crack in a brittle material. The edge of the propagating crack is nominally straight; the wave corresponds to a small perturbation from straightness. Symmetric (Mode I) loading is assumed. The fracture criterion is the Griffith energy balance (so that energy is conserved). E Sharon observed traces on fracture surfaces in glass that definitely correspond to long-lasting disturbances, and thus provide supporting evidence for the existence of a crack front wave. The same experiment in plexiglass shows traces that attenuate, suggesting that a crack front wave in such material be modified by a dissipative mechanism. Analytic confirmation of the existence of crack front waves was provided by Ramanathan and Fisher, who verified the presence of a pole in a transfer function relating crack shape perturbation to energy flux perturbation. The transfer function followed directly from the complete solution to the problem of the dynamic perturbation of a moving crack front by Movchan and Willis.
The theory of Movchan and Willis will be summarized, and the transfer function developed. A more recent extension, not yet published, provides the corresponding solution for propagation in a viscoelastic medium. This will also be outlined (the calculation for the attenuation of the crack front wave is in progress). The Movchan/Willis theory has also been developed for mixed Mode II/III propagation. It is again possible to seek possible crack front waves in this situation, which might be relevant, for example, in the seismic context. Results obtained so far are surprising and need detailed checking before any definite pronouncement can be made. These results will, nevertheless, be shared with the audience.

We are developing experiments on intense laser facilities to study shock compressed metal foils in the solid state.  At high pressure, Rayleigh-Taylor induced perturbation growth can be reduced by the strength of the material. [1] We use this to characterize the strength of the metal foils accelerated at high pressure in the solid state.
In our experiments, Al and Cu foils are compressed and accelerated with staged shocks using a temporally shaped x-ray drive that is generated in a Nova laser hohlraum target. [2] The peak pressures exceed 1 Mbar (100 GPa), and strain rates are very high, 1e7-1e9 /s.  The instability growth is observed by x-ray radiography.
To probe the state of the material under compression and to demonstrate that it remains solid, we are using the dynamic Bragg diffraction technique. [3] This technique has been demonstrated on the Nova laser [4] using Si crystals shocked to 200-500 kbar. Additionally, we have observed diffraction from Cu crystals that are shocked to 100-200 kbar by direct laser irradiation on the Trident and OMEGA lasers. Compressions of up to a 10% in the crystal lattice spacing have been observed.
Results of this work to develop high-pressure solid-state hydrodynamics experiments will be presented.
1. J. F. Barnes et al, J. Appl. Phys. 45, 727 (1974); A. I. Lebedev et al , Proc. 4th IWPCTM, 29 March-1 April, 1993, p. 81.
2. D. H. Kalantar et al., Phys. Plasmas 7, 1999 (2000).
3. R. R. Whitlock and J. S. Wark, Phys. Rev. B 52, 8 (1995).
4. D. H. Kalantar et al, Rev. Sci. Instrum. 70, 629 (1999).
* This work was done in collaboration with J. D. Colvin, D. M.  Gold,
K. O. Mikaelian, B. A. Remington, S. V. Weber, L. G. Wiley,
A. M. Allen, A. Loveridge, J. S. Wark, T. R. Boehly, A. A. Hauer,
D. Paisley, M. A. Meyers.  It was performed under the auspices of the
US DOE by UC LLNL under Contract No. W-7405-ENG-48.

Models proposed for the formulation and annealing twins will be briefly reviewed.  It will be shown that embryonic deformation twins form by a reaction between two a/z<110> dislocations that have co-planar Burgers vectors.  Microscopic twins evolve by the coalescence of the embryonic twins that are located at different levels within slip bands.  The observed relationship between the crystallographies of twinning and associated slip is consistent with the preceding suggestion and is not compatible with the pole model.  In addition, the orientation dependence of twinning can be rationalized in terms of the proposed model.

It will be argued that grain boundary migration is necessary for the formation of annealing twins.  These twins are a result of growth accidents occurring on {111} facets of migrating boundaries.  This conceptual framework is a hybrid of the Gleiter and Meyers-Murr models.  Details of the mechanism will be presented and the influence of temperature and stacking fault energy on the incidence of twinning will be discussed.

Subhash Mahajan is Professor of Electronic Materials and Interim Chair of the Department of Chemical and Materials Engineering at Arizona State University.  He obtained his undergraduate education in India and then attended the University of California at Berkeley for his graduate studies.  After completing his Ph.D., he held positions at the University of Denver, The Atomic Energy Research Establishment in Harwell, England, AT&T Bell Laboratories at Murray Hill, New Jersey and Carnegie Mellon University.  He joined Arizona State University in 1997.  He was also visiting professor at the University of Antwerp and the Ecole' Central de Lyon.

Professor Mahajan's research focuses on understanding the origins of defects in semiconductors and their influence on device behavior and deformation behavior of solids.  He has published extensively on these topics.  Professor Mahajan edits a number of journals and has edited and co-edited The Handbook on Semiconductors and The Encyclopedia of Advanced Materials.  Currently, he is serving as one of the Editors-in-Chief of The Encyclopedia of Materials: Science and Technology, to be published by Elsevier in 2001.  He has also written an undergraduate textbook on the Principles of Growth and Processing of Semiconductors.

Professor Mahajan received the John Bardeen Award and the Albert Sauveur Achievement Award from TMS and ASM, respectively, recognizing his outstanding contributions to research and leadership in electronic materials and his pioneering achievements in materials science.  Recently, he was elected TMS Fellow.

The determination of fatigue crack propagation (FCP) rates in structural metal alloys is needed to compute available lifetimes in engineering components that experience cyclic loading conditions.  Additionally, closure-corrected FCP information has been found useful in assessing the intrinsic fatigue resistance of metal alloy systems, especially for conditions associated with the growth of physically short cracks.  This author has developed a simplified experimental method by which closure-corrected FCP data may be easily and conveniently determined.  More recently, this author has demonstrated that these experimental data can be predicted, based on a simple computational method involving the use of only two basic material constants-- the modulus of elasticity, E, and the dislocation Burgers vector, b.

There are now some 14,000 passenger aircraft in commercial service in the U.S., a number that must double by the year 2016 in order to carry a projected one billion passengers annually.  If the present rate of hull loss remains unchanged, there will be a passenger aircraft lost every week.  Exacerbating this unacceptable situation, because future demands for air travel will require more new aircraft than the nation's aircraft manufacturing capacity can provide, the present fleet will need to be operated much longer than originally intended.  Given that the average age of the nation's commercial aircraft fleet is already 75% of its nominal 20 year design life, significant attention is now being given to understanding and quantifying aircraft "aging" problem that, if uncorrected, could lead to a significant increase in the current rate of hull loss.  The technology that underlies this activity is the engineering discipline of fracture mechanics.

This lecture will first trace the history of aircraft structural integrity analysis methods from fail safe to safe life to damage tolerance to probabilistic fracture mechanics  This progression will show both the pivotal role played by fracture mechanics in aircraft integrity and the key role that the aviation industry has played in its development.  With this backdrop, emphasis will be placed on outlining new fracture mechanics related research challenges arising from multiple site damage, combined fatigue and corrosion crack growth, the containment of large scale discrete source damage, and other complex manifestations of aircraft aging.

J.R. Rice discovered, during computer simulation, the existence of a wave that could propagate, apparently without change of form and without attenuation, along the edge of a propagating crack in a brittle material.  The edge of the propagating crack is nominally straight; the wave corresponds to a small perturbation form straightness.  Symmetric (Mode I) loading is assumed.  The fracture criterion is the Griffith energy balance (so that energy is conserved).  E. Sharon observed traces on fracture surfaces in glass that definitely correspond to long-lasting disturbances, and thus provide supporting evidence for the existence of a crack front wave.  The same experiment in plexiglass shows traces that attenuate, suggesting that a crack front wave in such material is modified by a dissipative mechanism.  Analytic confirmation of the existence of crack front waves was provided by Ramanathan and Fisher, who verified the presence of a pole in a transfer function relating crack shape perturbation to energy flux perturbation.  The transfer function followed directly from the complete solution to the problem of the dynamic perturbation of a moving crack front by Movchan and Willis.

The theory of Movchan and Willis will be summarized, and the transfer function developed.  A more recent extension, not yet published, provides the corresponding solution for propagation in a viscoelastic medium.  This will also be outlined (the calculation for the attenuation of the crack front wave is in progress).  The Movchan/Willis theory has also been developed for mixed Mode II/III propagation.  It is again possible to seek possible crack front waves in this situation, which might be relevant, for example, in the seismic context.  Results obtained so far are surprising and need detailed checking before any definite pronouncement can be made.  These results will, nevertheless, be shared with the audience.

My colleagues and I have constructed a model of the hydroskeleton of the medicinal leech, based upon measurements of the mechanical properties and geometric arrangements of its muscles.  The body of a leech is essentially a compartmented tube with muscles in its walls, which surround incompressible fluids.  The two major muscle masses are arranged longitudinally and circularly; they cause shortening and elongation of the tubular body.  The model was tested by predicting the pressures generated within the body during different behavioral acts (shortening, crawling, swimming); these were subsequently verified by direct measurements in behaving animals.  We then used motor neuron patterns measured in behaving animals to drive the model to see how realistically the model simulated behaviors.  This exercise indicated that (1) Crawling behaviors must depend upon sensory feedback to produce normal stepping; and (2) We need to understand the dynamic behavior of leech muscles before we can simulate swimming.  This talk will emphasize the interaction between biomechanical models and physiological experiments, and will present a model that should be relevant for understanding movements in such hydroskeletons as our own tongues and intestines.

Methods for incorporating discontinuities in meshfree methods and in finite element methods are described.  These are useful for modeling cracks, phase interfaces and other phenomena.  In meshfree methods, discontinuities are easily incorporated through the visibility criterion, although this method introduces discontinuities in the field around the end of the crack tip.  Methods for smoothing these discontinuities are described.  For finite elements, new methods for embedding discontinuities independent of the mesh geometry are described.  The discontinuities are embedded through a partition of unity, which maintains the sparsity of the discrete equations.  Both discontinuities in the function and its derivatives are treated.  Simplified methods which employ the concept of level sets are also described.  Applications in crack growth are reported.

Coherent scattering and diffraction were used for identification of crystalline substances for decades and are known as Powder Analysis in chemistry, metallurgy and mining industry. In vitro studies have established that biological materials, such as glandular tissue, muscle, mucus, fat, hair, cartilage and bones, have semi-crystalline molecular structures and relatively unique scattering patterns. That is made possible to distinguish between different tissues and even between different physiological states of tissue. Diffraction patterns of muscle and cartilage are distinctly different and differences are readily detectable when recorded on film or digital record. Contracted muscle and relaxed muscle have different diffraction patterns that convey information about level of contraction and hence on physiological status of the muscle.

Conventional diagnostic x-ray imaging methods (including radiography, fluoroscopy and CT) measure differences in attenuation between different points in an object, which provides information that depends on the density and average atomic number of the tissue. In diagnostic imaging, scatter is treated as a complication since it increases the noise and reduces the contrast in transmission measurements. However, coherent scattering contains important information about the molecular structure (as opposed to atomic composition and density).

Recent work by Quanta Vision prototype ULAX system has demonstrated the high sensitivity of small-angle x-ray scattering for differentiation among small tissue samples, including between normal tissue, benign lesions, and early cancer in the breast.

An initio study of the electronic structure of the solid explosive RDX crystal containing the [001] edge dislocations was performed by means of the Hartree-Fock periodic method combined with the many-body perturbation theory. Additionally, we have studied how strong compression (for example, shock/impact wave) affects the RDX crystal with edge dislocations. We found that an external pressure causes a significant decrease of the optical gap for both the perfect material and the crystal with dislocations. The edge dislocations produce local electronic states in the optical gap whereas the external pressure moves these states deep within the band gap. This contributes strongly to properties of the RDX crystals creating favorable conditions for the N-NO2 chemical bond rupture due to exciton formation. Relations between the edge dislocations, hot spots formation, and the sensitivity of RDX to detonation are discussed in detail. A new mechanism of detonation initiation is proposed.

The essential conclusion is that edge dislocations in the RDX crystal could serve as hot spots, which are characterized by a local internal stress and by a reduced optical gap. The impact wave propagating through the crystal stimulates a further dramatic gap reduction increasing the probability of electron excitation. This, in turn causes molecular dissociation via an excitonic mechanism and start a chain reaction and explosion.

The FRAGBED2 model for comminution and flow of ceramics undergoing dynamic compressive loads will be presented. The model has been tested against data from cylinder compaction experiments designed by Nesterenko and Klopp, and against long rod penetration data. The agreement is good for the penetration data, but ambiguous for the cylinder compaction data. We will discuss especially the comminution part of the model, and the model's potential for describing localization of flow resulting from comminution-driven softening.

The human vascular system, comprised of the blood vessels, supplies each tissue with blood at a given rate and pressure. To understand both the normal and pathological behavior of the human vascular system a detailed knowledge of blood flow and the response of blood vessels is required. Blood flow characteristics have a controlling influence in the development of plaque deposits and surgical procedures which alter the division of flow among blood vessels often have unforeseen consequences. This talk presents an overview of research on the computational modeling of blood flow performed at Stanford University. A computer modeling environment has been developed for simulating blood flow in the vascular system. Case studies involving idealized and patient specific configurations will be presented and a future vision of surgical simulation and planning will be described.

For further information see: http://www.stanford.edu/group/vsrl/

* This seminar is sponsored jointly by Mechanics and Materials Engineering and Fluid Mechanics.

A fundamental concept in continuum mechanics is that of a Representative Volume Element (RVE). As elucidated by Hill 1963, it states that the relations between volume average stress and strain should be the same regardless of whether uniform kinematic or uniform stress boundary conditions have been used. The point is that large volumes of material need to be considered to remove the effect of type of boundary conditions, and, for smaller volumes, a mesoscale Statistical Volume Element (SVE) is needed. The SVE plays a fundamental role in the setup of random continuum models of heterogeneous media. In turn, the latter provide a stepping-stone to micromechanically-based stochastic finite elements (SFE), plastic slip-lines, etc.. This is in contrast to the conventional SFE, which randomize the Hooke's law directly, and thus, lack any connection to the underlying material microstructures. We next look at transient wave propagation. Given the microscale material randomness, the wavefront is seen as a zone of finite thickness rather than a classical discontinuity surface - yet another paradigm for the SVE concept (Ostoja-Starzewski and Trebicki 1999). In the case of the wavefront thickness being finite relative to the grain size, fluctuations are significant and not negligible; the wavefront evolution is then governed by a stochastic dynamical system. Time permitting, we will also report on some research on homogenization problems for wave propagation and structural dynamics, namely: SFE in the frequency domain.